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Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Witch of Agnesi

Age 16 to 18 Challenge Level:

Sketch the members of the family of graphs given by $$y = {a^3\over (x^2+a^2)}$$ for $a=1$, $2$ and $3$.
Greyscale image of a witch